The Leaky Cauldron

I'm not sure his house was ever mentioned in the books, but it was confirmed on Pottermore later:

Sorted into Ravenclaw house, Lockhart was soon achieving good marks in his schoolwork, but there was always a kink in his nature that made him increasingly unsatisfied. If he was not first and best, he would rather not participate at all. Increasingly, he directed his talents towards short cuts and dodges. He valued learning not for its own sake, but for the attention it brought him. He craved prizes and awards. He lobbied the Headmaster to start a school newsletter, because he liked nothing better than to see his name and photograph in print.

He's an interesting Ravenclaw. Smart, and a good student, but with unhealthy motivation.